Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ESTIMATES FOR EIGENVALUES OF NEUMANN AND NAVIER PROBLEM

  • Deng, Yanlin (School of Mathematics and Physics Science Jingchu University of Technology and Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University) ;
  • Du, Feng (School of Mathematics and Physics Science Jingchu University of Technology and Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University) ;
  • Hou, Lanbao (School of Mathematics and Physics Science Jingchu University of Technology and Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University)
  • Received : 2020.02.22
  • Accepted : 2021.02.18
  • Published : 2021.11.30
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Abstract

In this paper, we firstly prove some general inequalities for the Neumann eigenvalues for domains contained in a Euclidean n-space ℝn. Using the general inequalities, we can derive some new Neumann eigenvalues estimates which include an upper bound for the (k + 1)th eigenvalue and a new estimate for the gap of the consecutive eigenvalues. Moreover, we give sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator with Navier boundary condition on compact Riemannian manifolds with boundary and positive Ricci curvature.

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Acknowledgement

This work was financially supported by Research Team Project of Jingchu University of Technology (Grant No. TD202006), Research Project of Jingchu University of Technology (Grant No. YB202010, ZX202002, ZX202006), and Hubei Key Laboratory of Applied Mathematics (Hubei University).

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